MATH 613—S Evaluation
Geometry and Measurement: K - 8 Learning and Teacher Practices
S Math Task 1: Quilt Patch Designs STUDENT ANSWERS
For each student, Susan and Donna, answer the following, you may group your answers if
you like.
1. What misconceptions, if any, does the child have? Can you relate this to a van Hiele
level?
2. What in the learning trajectory understanding, before this task, is this student missing?
Susan
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My shape is a person
My shape has 11 blocks
My shape has 3 hexagons, 3 triangles, 2 diamonds and 2 squares
My shape is symmetrical down the middle from the top to the
bottom
2 of the triangles are feet and 1 is a hat
The arms start with a diamond and end with a square
My shape has five colors
Donna
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Parallelograms
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Rhombi
I can make squares, rectangles, rhombi, parallelograms,
trapezoids and lots of plain quadrilaterals with the
pattern blocks
All of the squares and rectangles are the same because
they can only be made of the orange squares
All of the parallelograms are long and skinny
All of the rhombi made with rhombi are congruent
because they have the same parts
Some of the trapezoids are isosceles but one is the house
kind of trapezoid
Squares and rectangles
Plain quadrilaterals
Trapezoids
MATH 613—S Evaluation
Geometry and Measurement: K - 8 Learning and Teacher Practices
S Math Task 2: Decomposing and Composing Shapes with Geoboards STUDENT ANSWERS
For each student, Jesse, Daniel and Nils, answer the following, you may group your answers
if you like.
1.
What misconceptions, if any, does the child have? Can you relate this to a van Hiele level?
2.
What in the learning trajectory understanding, before this task, is this student missing?
JESSE
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Divide this shape into three triangles that are all the same. Explain how
you know they are the same triangle. Can you do this in more than one
way?
I know these triangles are all the same in my first picture because they can
all be broken into two parts that are the same.
In my second picture, if you put the red pieces together, you get another
way to divide the trapezoid into three triangles that are the same. They
are the same because they all have the same height.
DANIEL
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What is the fewest number of triangles that will fill this shape? Explain
how you know. Can you do this in more than one way?
I needed ten triangles to fill it and they are all the same since they have
the square corner
When I do it the other way I need twelve triangles, so ten is the minimum
NILS
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Make a shape that is not a rectangle on your geoboard
using four non-square rectangles that are all the same
and then re-divide your shape in a different way using
four rectangles that are all the same. Use a shape that
can be composed of four rectangles in at least two ways.
I can do it in two ways but the second is better because
the outside shape is not a rectangle.
MATH 613—S Evaluation
Geometry and Measurement: K - 8 Learning and Teacher Practices
S Math Task 3: Solids and Nets STUDENT ANSWERS
For each student, Tyler, Jillian and Joy, answer the following, you may group your answers if
you like.
1.
What misconceptions, if any, does the child have? Can you relate this to a van Hiele level?
2.
What in the learning trajectory understanding, before this task, is this student missing?
TYLER I put my names below each shape
Rectangle
pyramid
Cylinder
Trapezoid prism
Cone
Box
Oblique
rectangle prism
Right triangle
pyramid
Hexagon
pyramid
Triangle
pyramid
JILLIAN Here are some of my nets
Trapezoid prism
Rectangle prism
Hexagon pyramid
Triangle pyramid
JOY Here are the names of the pieces of my nets
Trapezoid prism
Cone
Hexagon pyramid
Trapezoid
Triangles
Cicrle
Trapezoid
Square
Trapezoid
Trapezoid Square
Triangles
Octagon
Oblique rectangle
prism